Render depth map to image with python script
From various sources I found out how to assemble a render graph to put out the depth map (scaled to the range [0, 255]):

# Set up rendering of depth map:
bpy.context.scene.use_nodes = True
tree = bpy.context.scene.node_tree
links = tree.links

# clear default nodes
for n in tree.nodes:
    tree.nodes.remove(n)

# create input render layer node
rl = tree.nodes.new('CompositorNodeRLayers')

map = tree.nodes.new(type="CompositorNodeMapValue")
# Size is chosen kind of arbitrarily, try out until you're satisfied with resulting depth map.
map.size = [0.08]
map.use_min = True
map.min = [0]
map.use_max = True
map.max = [255]
links.new(rl.outputs[2], map.inputs[0])

invert = tree.nodes.new(type="CompositorNodeInvert")
links.new(map.outputs[0], invert.inputs[1])

# The viewer can come in handy for inspecting the results in the GUI
depthViewer = tree.nodes.new(type="CompositorNodeViewer")
links.new(invert.outputs[0], depthViewer.inputs[0])
# Use alpha from input.
links.new(rl.outputs[1], depthViewer.inputs[1])


The output can then be saved to a file using a File Output node:

# create a file output node and set the path
fileOutput = tree.nodes.new(type="CompositorNodeOutputFile")
fileOutput.base_path = "/my_path/"
links.new(invert.outputs[0], fileOutput.inputs[0])


Whenever a render is triggered, the depth map will be dumped into the base_path specified.